During a visit to Sevastopol on February 21, Luzhkov promised support for ethnic Russians in Crimea and thanked the region for opposing Ukraine's efforts to cooperate with NATO.
Luzhkov also decried Soviet leader Nikita Khrushchev's turning over of Crimea -- where Russia's Black Sea Fleet is located -- to Ukraine in 1954.
Ukrainian officials accused Luzhkov of questioning Crimea's status as part of Ukraine.
Speaking at a joint press conference with acting Foreign Minister Volodymyr Ohryzko, Nalyvaichenko said Luzhkov could face a warning, a ban on entering the country, or more serious criminal penalties.
"A foreigner on the territory of our country, regardless of his status and citizenship, must respect the laws, the language, and the culture of the people," Nalyvaichenko said. "So, the [Ukrainian] reaction will be harsh, in accordance with the law."
Ohryzko said the Foreign Ministry and law enforcement bodies will assess the extent to which Luzhkov's comments threatened Ukraine's "territorial integrity and security."
(with material from Interfax)